We study the use of deep neural networks towards the prediction of the optical properties of two-dimensional photonic crystals, as well as their inverse design. We incorporate a rigorous tight-binding model as a known operator in the machine learning algorithm. This physics-informed approach allows the prediction of meaningful model parameters rather than the high-dimensional full response, allowing for an efficient method as well as potential insight in the physical workings of specific designs. We demonstrate a four-order-of-magnitude speedup of prediction of bandstructures and field symmetries over full-field calculations, and proof-of-concept inverse design of photonic crystals with large gaps, flat bands, and Dirac-point degeneracies.
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